Polar Coordinates

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Change of Coordinate Systems
Harmonic Warping

Polar Coordinates are coordinates which locate points by their distance from the origin and their rotation from the positive x-axis. Traditionally,  r represents distance from the origin and  \theta represents rotation in radians from the positive x-axis.

For example, the point  (x,y) = \left (\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}} \right ) is 1 unit from the origin (as can be seen by the Pythagorean Theorem) and is a rotation of  \tfrac{\pi}{4} from the positive x-axis, so can be represented in polar form by:  (r,\theta)= \left (1,\tfrac{\pi}{4} \right ) .

Locating a point using its distance from the origin and its rotation for the + x-axis